Four Simple Ways to Make Multiplication Make Sense

A child can recite 7×8 perfectly on Tuesday and completely blank on it by Thursday morning.

Meanwhile, you probably haven’t practiced 7×8 in years, but you just know the answer. It isn’t because you have a better memory. It’s because you’ve seen that number in so many different places that it has become a fact you recognize, like a face, rather than a problem you have to solve.

That’s why we want to move the focus from memorization to familiarity.

Memorizing is useful, but it only works until your child is tired, or stressed, or sees the same question written in a way they aren’t used to. When they actually see how multiplication works in their daily life, they have a real memory to fall back on. If they forget the answer, they don’t have to panic; they can just figure it out for themselves.

Kids probably already do these four things at school or while they’re playing at home. Sorting toys into equal piles, lining things up in rows, or making a drawing bigger are all just different ways of doing multiplication. They just haven’t linked those actions to a number problem like 4x3 yet. It is completely fine if only one of these ideas clicks for them. Every kid has their own way of making sense of it.

1. Equal Groups

The most familiar version is equal groups. You can find this in simple chores like setting the dinner table. If four people are eating, you need four glasses. A few nights later, you can make it slightly more complex. Ask your child to grab a fork and a knife for each of those four people. They get to figure out the total of eight utensils without feeling like it is a math test.

If you want a dedicated moment for this, put out a muffin tin and some pasta or coins. Roll a die twice: once for how many cups to fill, and once for how many objects go in each cup. Then figure out the total without counting every single piece.

2. Rows and Columns

Rows and columns give you another way to think about multiplication that is a bit different from just using equal groups. Think of egg cartons or muffin trays. They naturally organize things into neat grids of rows and columns. Often, children will count the whole tray one by one.

If they do, you can introduce a simple trick with some sticky notes. Hold the carton so it looks long and narrow. Have them look at just the top row. They will see it has two holes. Have them write “Row 1: 2 holes” on a sticky note and place it next to that row. Then move to the next one. It also has two holes. They can write “Row 2: 2 holes” and stick it down.

They can keep going all the way down to the sixth row. By labelling the rows this way, they can clearly see they have six rows with two holes in each. They can add those twos together instead of counting every single hole from scratch.

Now for the best part. Once they finish adding, physically spin the egg carton sideways. Suddenly, those six short rows become two long rows. Grab new sticky notes and have them label the new top row: “Row 1: 6 holes.” Then the bottom row: “Row 2: 6 holes.”

The carton never changed, and the total number of holes stayed exactly the same. But by labelling it both ways, they get to see with their own eyes why six times two is exactly the same as two times six. You don’t even need to teach the rule. Spinning the carton does the work for you.

3. The Constant Relationship

This is the idea that the relationship between two things stays the same even as the numbers get bigger. Making an omelette is a perfect example. If two eggs make one omelette, how many do you need for four people? Let them work it out. You can make it more interesting by changing the number of people each time and letting them figure out the new total of eggs.

Setting the table works the same way. One plate, one fork, and one glass for every person. The ratio of “stuff” to “people” never shifts. It just scales.

4. Multiplication as Scaling

The last idea is scaling. This is making something bigger or smaller by a certain factor. Instead of adding to a shape, you are transforming it. The best way to explore this is to reverse engineer it on some grid paper. Draw a tiny square that takes up one block, a medium one that is two blocks wide and two blocks tall, and a large one that is four blocks wide and four blocks tall.

Tell your child that the medium square is “two times bigger” than the small one, and the largest is “four times bigger.” Then, let them be the detective. Ask them to find out why that is. They will likely see that the sides are twice as long, but they might be surprised to see that the “two times bigger” square actually holds four small squares inside it. Once they have found your secret rule, ask them to draw a square that is three times bigger than the first one.

The Takeaway

These are just simple things to try in your daily life. But they are just as useful when your child is stuck. If they are staring at a multiplication problem and the answer won’t come, it is completely fine to step back and reach for something real. Lay out some crackers, set the table, or grab the grid paper. Going back to the concrete is not a step backwards. It is how understanding actually gets built.

The goal was never to memorize faster. It was to understand deeply enough that memorizing becomes the easy part.